"""
Problem 23: https://projecteuler.net/problem=23

A perfect number is a number for which the sum of its proper divisors is exactly
equal to the number. For example, the sum of the proper divisors of 28 would be
1 + 2 + 4 + 7 + 14 = 28, which means that 28 is a perfect number.

A number n is called deficient if the sum of its proper divisors is less than n
and it is called abundant if this sum exceeds n.

As 12 is the smallest abundant number, 1 + 2 + 3 + 4 + 6 = 16, the smallest
number that can be written as the sum of two abundant numbers is 24. By
mathematical analysis, it can be shown that all integers greater than 28123
can be written as the sum of two abundant numbers. However, this upper limit
cannot be reduced any further by analysis even though it is known that the
greatest number that cannot be expressed as the sum of two abundant numbers
is less than this limit.

Find the sum of all the positive integers which cannot be written as the sum
of two abundant numbers.
"""

# _*_ conding:UTF-8 _*_
'''
@author = Kuperain
@email = kuperain@aliyun.com
@IDE = Thonny Python3.8.3
@creat_time = 2022/5/9
'''

from p021 import sumProperDivisors  #

def classify(n: int) -> str :
    '''
    12 is the smallest abundant number
    >>> min([x for x in range(1,100) if classify(x) == 'abundant'])
    12
    >>> assert classify(28) == 'perfect'
    '''
    spd_n = sumProperDivisors(n)
    
    if spd_n == n:
        return 'perfect'
    elif spd_n < n:
        return 'deficient'
    else:
        return 'abundant'


def decompose(n: int):
    '''
    all integers greater than 28123 can be written
    as the sum of two abundant numbers
    
    >>> assert all(map(decompose,range(28123,28199)))
    >>> decompose(24)
    12
    >>> decompose(28122)
    12
    '''
    
    for i in range(12, n//2 + 1):  # 12 is the smallest abundant number
        if classify(i) == 'abundant' and classify(n-i) == 'abundant':
            # print(f'{n} = {i} + {n-i}')
            return i
    
    return False


def solution(maxNum: int = 28123) -> int :
    '''
    the sum of all the positive integers which cannot be written as
    the sum of two abundant numbers
    '''
    # return sum([x for x in range(maxNum+1) if not decompose(x)])
    
    res = 0
    for x in range(1, maxNum+1):
        if x % (maxNum // 50) == 0:
            print('▓' * (x // (maxNum // 50)), f'{100*x//maxNum}%')
        if not decompose(x):
            # print(x)
            res += x
    
    return res

    

if __name__ == "__main__":
    import doctest
    doctest.testmod(verbose = False)
    
    print(solution())
    # 4179871

    
    
    
    


    


